2015 EdExcel A Level Physics Topic 4 Fluid dynamics and Stokes’ Law Laminar Flow vs Turbulent Flow Fluid mechanics 9/17/2018 Laminar Flow vs Turbulent Flow Laminar flow (seen here) is when “adjacent layers of a fluid do not cross over each other”. Turbulent flow is when “layers of fluid cross over each other”. This can happen when the rate of flow reaches a critical level (or, obviously, when obstacles are put in the way…). 17/09/2018 Laminar Flow vs Turbulent Flow Laminar flow (seen here) is when “adjacent layers of a fluid do not cross over each other”. Turbulent flow is when “layers of fluid cross over each other”. This can happen when the rate of flow reaches a critical level (or, obviously, when obstacles are put in the way…). 17/09/2018 Stokes’ Law When a sphere moves through a liquid the movement of the liquid relative to the sphere is laminar. This can be expressed mathematically…… Consider a sphere of radius r moving with a velocity v relative to a fluid with viscosity η: Viscous drag Fd = 6πηrv This is called Stokes’ Law, after Viscous me. It ONLY works for spheres drag moving at low speeds (i.e. laminar flow) Example Calculate the drag force on a sphere of radius 5 cm an it is travelling in a liquid having viscosity 2.2x10-3 N s m-2 with a velocity 25 ms-1. 17/09/2018 Example Calculate the drag force on a sphere of radius 5 cm an it is travelling in a liquid having viscosity 2.2x10-3 N s m-2 with a velocity 25 ms-1. Solution: r=0.05 m v= 25 ms-1 η= 2.2x10-3 Nsm-2 Viscous drag F = 6πηrv By putting in the values F = 6 x 3.14 x 2.2x10-3 x 0.05 x 25=51.81x10-3 N 17/09/2018 Terminal Velocity When vehicles and free-falling objects first move they have much more force accelerating them than resistance which is trying to slow them Body As speed increases resistance builds released Forces on up – gradually reducing the resultant from body during Forces on force and so the acceleration also rest acceleration body at reduces terminal velocity Eventually the resistance forces are equal to the accelerating force and the object remains at a constant speed (terminal velocity). Terminal Velocity Forces acting on a skydiver Weight, W=mg Upthrust, U Viscous drag, Fv Fv U At terminal velocity the resultant force ƩF=0 ƩF = 0 = W – (U + Fv) W a= ƩF/m = 0 acceleration is zero! 17/09/2018 Terminal Velocity in a liquid Consider a ball falling through a liquid: Some questions to consider: 1) What forces are acting on the ball? 2) How do those forces change when the ball gets faster? 3) Will the ball keep getting faster? Explain your answer in terms of forces 17/09/2018 Terminal Velocity What forces are acting on the ball? Some facts about the sphere falling through a fluid: 1) The weight, obviously, stays constant Upthrust Viscous 2) Upthrust = weight of fluid displaced, so U drag F that stays constant after the sphere becomes totally immersed Weight W 3) Viscous drag is proportional to velocity so it increases as the ball gets faster Clearly, terminal velocity is reached when the following condition is met: ƩF= 0 = W – (U + F) W = U + F 17/09/2018 Free body force diagrams Draw free body force diagrams and write a force equation for the following objects: 1) A ball bearing with a density just less than water floating on its surface: 2) A more dense ball bearing accelerating through a liquid: 3) The same ball bearing later when it has reached terminal velocity: 17/09/2018 Free body force diagrams Draw free body force diagrams and write a force equation for the following objects: 1) A ball bearing with low density that’s accelerating towards the surface: 2) The same ball bearing when it has reached terminal velocity while rising: 3) The same ball bearing later when it has reached the surface: 17/09/2018 Core Practical 4 - Viscosity The viscosity of a fluid can be defined as its “resistance to flow”, i.e. a viscous fluid is one that would be thick and sticky (like syrup). Comparing viscosities The viscosity of different fluids can be compared by using a viscometer or by dropping a ball bearing through the liquid: 17/09/2018 Example A steel ball-bearing of mass 2.6x10-4kg and radius 4.0mm is allowed to fall through water until it reaches terminal velocity. Calculate this terminal velocity if the viscosity of water is 2.2x10-3 N s m-2. Solution: m= 2.6x10-4kg r= 4.0mm= 4x10-3m upthrust η= 2.2x10-3 Nsm-2 drag force v=? Drag Force: F = 6πηrv By putting values F = 6 x 3.14 x 2.2x10-3 x 4x10-3 x v=1.66 x10-4 v Newton weight Example cont. 푢푝푡ℎ푟푢푠푡 푢푝푡ℎ푟푢푠푡 = 푑푒푛푠푡푦 표푓 푤푎푡푒푟 푥 푣표푙푢푚푒 표푓 푤푎푡푒푟 푑푠푝푙푎푐푒푑 푥푔 4 푣표푙푢푚푒 표푓 푤푎푡푒푟 푑푠푝푙푎푐푒푑 = 휋푟3 3 4 푣표푙푢푚푒 표푓 푤푎푡푒푟 푑푠푝푙푎푐푒푑 = 푥3.14푥(4푥10−3)3 = 2.717푥10−8푚3 3 푢푝푡ℎ푟푢푠푡 = 1000 푥2.717푥10−8푥 9.8 = 2.66푥10−4푁 Weight of ball 푤 = 푚푔 푤 = 2.6 x10−4푥9.8 = 2.548x10−3푘푔푚푠-2 terminal velocity is reached when the following condition is met: W = U + F 2.548x10−3 = 2.66푥10−4 + 1.66 x10−4푣 2.282x10−3 = 1.66 x10−4푣 v=13.75푚푠-1 Practice Questions 1) A steel ball-bearing of mass 1.1x10-4kg and radius 1.8mm is allowed to fall through water until it reaches terminal velocity. Calculate this terminal velocity if the viscosity of water is 1.1x10-3 N s m-2. 2) A ball of density 8000 kgm-3 and radius 1.2mm is allowed to fall through water until it reaches terminal velocity. Calculate this terminal velocity if the viscosity of water is 1.1x10-3 N s m-2. 17/09/2018.